Orders of Rectification
A first order rectification truncates edges down to points. If a polytope is regular, this form is represented by an extended Schläfli symbol notation t1{p,q,...}.
A second order rectification, or birectification, truncates faces down to points. If regular it has notation t2{p,q,...}. For polyhedra, a birectification creates a dual polyhedron.
Higher order rectifications can be constructed for higher order polytopes. In general an n-rectification truncates n-faces to points.
If an n-polytope is (n-1)-rectified, its facets are reduced to points and the polytope becomes its dual.
Read more about this topic: Rectification (geometry)
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